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1.
This Letter is devoted to the existence of the random attractor of stochastic Klein-Gordon-Schödinger equations in an infinite lattice. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor. 相似文献
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Evidence is presented for the nonchaotic random behaviour in a
second-order autonomous deterministic system. This behaviour is
different from chaos and strange nonchaotic attractor. The
nonchaotic random behaviour is very sensitive to the initial
conditions. Slight difference of the initial conditions will
generate wholly different phase trajectories. This random behaviour
has a transient random nature and is very similar to the
coin-throwing case in the classical theory of probability. The
existence of the nonchaotic random behaviour not only can be derived
from the theoretical analysis, but also is proved by the results of
the simulated experiments in this paper. 相似文献
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M S Gopinathan 《Pramana》1997,49(6):581-590
The space overlap of an attractor reconstructed from a time series with a similarly reconstructed attractor from a random series is shown to be a sensitive measure of determinism. Results for the time series for Henon, Lorenz and Rössler systems as well as a linear stochastic signal and an experimental ECG signal are reported. The overlap increases with increasing levels of added noise, as shown in the case of Henon attractor. Further, the overlap is shown to decrease as noise is reduced in the case of the ECG signal when subjected to singular value decomposition. The scaling behaviour of the overlap with bin size affords a reliable estimate of the fractal dimension of the attractor even with limited data. 相似文献
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González-Miranda JM 《Chaos (Woodbury, N.Y.)》2003,13(3):845-852
Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh-Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors. 相似文献
8.
I. Belykh V. Belykh R. Jeter M. Hasler 《The European physical journal. Special topics》2013,222(10):2497-2507
We consider oscillators whose parameters randomly switch between two values at equal time intervals. If random switching is fast compared to the oscillator’s intrinsic time scale, one expects the switching system to follow the averaged system, obtained by replacing the random variables with their mean. The averaged system is multistable and one of its attractors is not shared by the switching system and acts as a ghost attractor for the switching system. Starting from the attraction basin of the averaged system’s ghost attractor, the trajectory of the switching system can converge near the ghost attractor with high probability or may escape to another attractor with low probability. Applying our recent general results on convergent properties of randomly switching dynamical systems [1, 2], we derive explicit bounds that connect these probabilities, the switching frequency, and the chosen initial conditions. 相似文献
9.
通过对改进恒Lyapunov指数谱混沌系统进行进一步演变,并引入新的绝对值项,发现了一种新的混沌吸引子.首先,通过相图、Poincar映射、Lyapunov指数以及功率谱,证明该混沌吸引子的存在性.接着,分析研究了这种新型混沌吸引子的基本动力学行为.Lyapunov指数谱、分岔图和状态变量幅值演变的数值仿真说明,该系统存在全局线性调幅参数,在该参数的调整下,系统输出三维信号的幅度皆能得到线性调整,而系统保持相同的混沌吸引子与Lyapunov指数谱.最后,通过构建电路实现了该混沌系统,观察到相应的混沌吸引子,也验证了全局线性调幅参数的调幅作用,数值仿真与电路实现有很好的一致性. 相似文献
10.
A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous
system 总被引:2,自引:0,他引:2
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This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic
cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through
theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization. 相似文献
11.
Experiments performed in a thin layer of the Belousov-Zhabotinsky solution subjected to a global feedback demonstrate the existence of the resonance attractor for meandering spiral waves within a domain of circular shape. In an elliptical domain, the resonance attractor can be destroyed due to a saddle-node bifurcation induced by a variation of the domain eccentricity. This conclusion explains the experimentally observed anchoring of spiral waves at certain points of an elliptical domain and is in good quantitative agreement with numerical data obtained for the Oregonator model. 相似文献
12.
We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. 相似文献
13.
We prove the existence of a random global attractor for the multivalued random dynamical system associated to a nonlinear multivalued parabolic equation with a stochastic term of amplitude of the order of . The equation was initially suggested by North and Cahalan (following a previous deterministic model proposed by M.I. Budyko), for the modeling of some non-deterministic variability (as, for instance, the cyclones which can be treated as a fast varying component and are represented as a white-noise process) in the context of energy balance climate models. We also prove the convergence (in some sense) of the global attractors, when , i.e., the convergence to the global attractor for the associated deterministic case (). 相似文献
14.
We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY3(2,128) expressed as a degree‐12 hypersurface in WCP 4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non‐supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C 8 which may also be “arithmetic” (in some cases, it is possible to interpret the extremization conditions for the black‐hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non‐supersymmetric black‐hole attractors corresponds to a version of A1‐singularity in the space Image( Z 6→ R 2/ Z 2 (↪ R 3)) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP 5→ CP 20, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black‐hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential. 相似文献
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We consider the critical behavior at the threshold of black-hole formation for the five-dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discretely self-similar solution with two unstable modes. 相似文献
17.
《Physica D: Nonlinear Phenomena》1988,32(3):423-436
Bifurcation in symmetric is typically associated with spontaneous symmetry breaking. That is, bifurcation is associated with new solution having less symmetry.In this paper we show that symmetry-increasing bifurcation in the discrete dynamics of symmetric mappings is possible (and is perhaps generic). The reason for these bifurcations may be understood as follows. The existence of one attractor in a system with symmetry gives rise to a family of conjugate attractors all related by symmetry. Typically, in computer experiments, what we see is a sequence of symmetry-breaking bifurcations leading to the existence of conjugate chaotic attractors. As the bifurcation parameter is varied these attractors grow in size and merge leading to a single attractor having greater symmetry.We prove a theorem suggesting why this new attractor should have greater symmetry and present a number of striking examples of the symmetric patterns that can be formed by iterating the simplest mappings on the plane with the symmetry of the regular m-gon. In the last section we discuss period-doubling in the presence of symmetry. 相似文献
18.
A mathematical model is constructed of a nonautonomous dynamic system containing a nonlinear capacitance and possessing a
four-dimensional phase space. A numerical investigation is performed of branching processes and phenomena accompanying variations
in the frequency and amplitude of an external force. The existence of complex dynamic processes that are a combination of
a nonlinear force resonance and a parametric resonance is demonstrated. It is found that both a strange chaotic and a strange
nonchaotic attractor exist in the phase space. It is shown that, in the case of a single-frequency external force, the latter
attractor exhibits the property of roughness. The results of numerical calculations are confirmed by the results of laboratory
experiments. 相似文献
19.
On the Strongly Damped Wave Equation 总被引:6,自引:0,他引:6
We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in the presence of a quite general nonlinearity of critical growth. When the nonlinearity is subcritical, we prove the existence of an exponential attractor of optimal regularity, having a basin of attraction coinciding with the whole phase-space. As a byproduct, the universal attractor is regular and of finite fractal dimension. Moreover, we carry out a detailed analysis of the asymptotic behavior of the solutions in dependence of the damping coefficient.Research partially supported the Italian MIUR Research Projects Problemi di Frontiera Libera nelle Scienze Applicate, Aspetti Teorici e Applicativi di Equazioni a Derivate Parziali and Metodi Variazionali e Topologici nello Studio dei Fenomeni Nonlineari. The second author was also supported by the Istituto Nazionale di Alta Matematica F. Severi (INdAM). 相似文献
20.
H. Shigematsu 《Journal of statistical physics》1990,59(1-2):257-297
The static and dynamic properties of a chaotic attractor of a two-dimensional map are studied, which belongs to a particular class of piecewise continuous invertible maps. Coverings of a natural size to cover the attractor are introduced, so that the microscopic information of the attractor is written on each box composing the cover. The statistical thermodynamics of the scaling indices and the size indices of the boxes is formulated. Analytic forms of the free energy functions of the scaling indices and the size indices of the boxes are obtained for examples of a hyperbolic and a nonhyperbolic chaotic attractor. The statistical thermodynamics of local Lyapunov exponents is also studied and a relation between the thermodynamics of scaling indices and of local Lyapunov exponents is invetigated. For the nonhyperbolic example, the free energy and entropy functions of local Lyapunov exponents are obtained in analytic forms. These results display the existence of phase transitions. A phase transition is seen in the thermodynamics of scaling indices also. 相似文献